Question

Determine the mass flow of nitrogen in an 8-in.-diameter duct if it has a velocity of 16 ft/s. The nitrogen has a temperature of 90∘F, and the gage pressure is 10 psi. The atmospheric pressure is 14.7 psi.

Answer 1

Answer:

Mass flow = 0.0203 slug/s

Explanation:

given data

diameter = 8 in

velocity = 16 ft/s

nitrogen temperature = 90°F = 549.67 °R

gage pressure = 10 psi

atmospheric pressure = 14.7 psi

solution

we know absolute pressure that is express as

$\rho$ absolute = $\rho$ gage + $\rho$ atmospheric    ....................1

put here value we get

$\rho$ absolute = 10 + 14.7

$\rho$ absolute = 24.7 psi

$\rho$ absolute = 3556.8 psf

and For nitrogen

R = 1775 ft-lb/slug °R

and we get gas equation that is express as  

$\rho$ absolute  = $\rho$ R T      ...............2

3556.8 = $\rho$ × 1775 × 549.67    

$\rho$ = 3.645 × $10^{-3}$  slug/ft³

so here Mass flow that is express as

Mass flow = $\rho$AV      .................3

Mass flow = 3.645 × $10^{-3}$  ×  ( $\frac{\pi \times (\frac{8}{12})^2}{4}$ ) ×  (16)

Mass flow = 0.0203 slug/s